Steve Johnson believes that this winter is going to be extremely rainy, and he is trying to decide whether he should repair or replace his roof. Steve can install a new roof for $7000 or have it repaired for $1000. While the repair work will probably mean that the house will not have any leaks during the upcoming year, Steve believes that he will definitely need a new roof next year and would have to pay $7000 at that time if he does not get the roof replaced this year. There is a 60% chance that Steve will be transferred during the upcoming year and will have to put his house on the market. Steve feels that a new roof will enable him to get $4000 more if he sells his house. If he does not repair or replace the roof, Steve believes there is a 70% change that there will be rain damage to his home. He estimates the likelihood that the damage will be $500 is 10%, $1000 is 20%, $1500 is 30%, and $2000 is 40%. Using a decision tree analysis, determine Steve’s optimal strategy for dealing with his roof.

Steve Johnson believes that this winter is going to be extremely rainy, and he is trying to decide whether he should repair or replace his roof. Steve can install a new roof for $7000 or have it repaired for $1000. While the repair work will probably mean that the house will not have any leaks during the upcoming year, Steve believes that he will definitely need a new roof next year and would have to pay $7000 at that time if he does not get the roof replaced this year. There is a 60% chance that Steve will be transferred during the upcoming year and will have to put his house on the market. Steve feels that a new roof will enable him to get $4000 more if he sells his house. If he does not repair or replace the roof, Steve believes there is a 70% change that there will be rain damage to his home. He estimates the likelihood that the damage will be $500 is 10%, $1000 is 20%, $1500 is 30%, and $2000 is 40%. Using a decision tree analysis, determine Steve’s optimal strategy for dealing with his roof.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 69P: The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon...

See similar textbooks

Similar questions

The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
Hemmingway, Inc., is considering a $5 million research and development (R&D) project. Profit projections appear promising, but Hemmingway's president is concerned because the probability that the R&D project will be successful is only 0.50. Furthermore, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $20 million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized. Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated $25 million. Under this option, the company would not build the $20 million production facility. The decision tree is shown in Figure 4.16. The profit projection for each outcome is shown at the end of the branches. For example, the revenue projection for the high demand outcome is $59 million.…
A farmer is trying to decide if continuing to farm is the correct thing to do. Yields on his fields have been declining over the past several seasons. He has an offer on the table from a corporate farmer to lease his land for the season for $15,000. Whether or not he accepts this offer depends on how well his fields will produce and the market value of his crops. If yield is high, the farmer will make $50,000 and there is a 10% possibility of this occurring. If yield is medium, the farmer will make $20,000 and there is a 50% possibility of this occurring. If yield is low, the farmer will make $12,000 and there is a 40% possibility of this occurring. Draw a decision tree for this problem. What should the farmer do according to the decision tree? If the farmer could get more information that would help him predict his yield, what is the maximum amount that he should pay for this information?
Hemmingway, Inc. is considering a $5 million research and development (R&D) project. Profit projections appear promising, but Hemmingway's president is concerned because the probability that the R&D project will be successful is only 0.50. Furthermore, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $20 million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized. Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated $25 million. Under this option, the company would not build the $20 million production facility. The decision tree follows. The profit projection for each outcome is shown at the end of the branches. For example, the revenue projection for the high demand outcome is $59 million. However, the cost of the R&D…
A real estate investor has the opportunity to purchase land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table: a. If the probability that the rezoning will be approved is 0.5, what decision is recommended? What is the expected profit? b. The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during the next three months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows: Let H = High resistance to rezoning L = Low resistance to rezoning P(H) = 0.55 P(S1 | H) =…
A real estate investor has the opportunity to purchase land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table: State of Nature Rezoning Approved Rezoning Not Approved Decision Alternative S1 S2 Purchase, d1 590 -160 Do not purchase, d2 0 0 If the probability that the rezoning will be approved is 0.5, what decision is recommended?Recommended decision: What is the expected profit?Expected profit: $ fill in the blank 2 The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during the next three months while learning more…
n September 2012, a 260,000 square foot Costco anchored shopping center was acquired in San Mateo, California for $36 million with a $26 million fully amortizing first mortgage loan from Union Bank. By 2018, the property had substantially appreciated in value and was worth $72 million and the owner wanted to access part or all of the increased equity value while paying little or no current taxes. The owner might: Refinance the property with a larger loan All these answers are correct Sell the property under an installment sale contract Trade the property for a property whose sale price is more than $54 million under Section 1031 of the Internal Revenue Code
Ellie Daniels has $200,000 and is considering three mutual funds for investment—a global fund, an index fund, and an Internet stock fund. During the first year of investment, Ellie estimates that there is a .70 probability that the market will go up and a .30 probability that the market will go down. Following are the returns on her $200,000 investment at the end of the year under each market condition: Market Conditions Fund Up Down Global $25,000 $ -8,000 Index 35,000 5,000 Internet 60,000 -35,000 At the end of the first year, Ellie will either reinvest the entire amount plus the return or sell and take the profit or loss. If she reinvests, she estimates that there is a .60 probability the market will go up and a .40 probability the market will go down. If Ellie reinvests in the global fund after it has gone up, her return on her initial $200,000 investment plus her $25,000 return after 1 year will be $45,000. If the market goes down, her loss will be $15,000. If she reinvests after…
Cheryl Druehl Retailers, Inc., must decide whether to build a small or a large facility at a new location in Fairfax. Demand at the location will either be low or high, with probabilities 0.3 and 0.7, respectively. If Cheryl builds a small facility and demand proves to be high, she then has the option of expanding the facility. If a small facility is built and demand proves to be high, and then the retailer expands the facility, the payoff is $290,000. If a small facility is built and demand proves to be high, but Cheryl then decides not to expand the facility, the payoff is $253,000. If a small facility is built and demand proves to be low, then there is no option to expand and the payoff is $220,000. If a large facility is built and demand proves to be low, Cheryl then has the option of stimulating demand through local advertising. If she does not exercise this option, then the payoff is $45,000. If she does exercise the advertising option, then the response to…
Cheryl Druehl Retailers, Inc., must decide whether to build a small or a large facility at a new location in Fairfax. Demand at the location will either be low or high, with probabilities 0.3 and 0.7, respectively. If Cheryl builds a small facility and demand proves to be high, she then has the option of expanding the facility. If a small facility is built and demand proves to be high, and then the retailer expands the facility, the payoff is $240,000. If a small facility is built and demand proves to be high, but Cheryl then decides not to expand the facility, the payoff is $213,000. If a small facility is built and demand proves to be low, then there is no option to expand and the payoff is $230,000. If a large facility is built and demand proves to be low, Cheryl then has the option of stimulating demand through local advertising. If she does not exercise this option, then the payoff is $60,000. If she does exercise the advertising option, then the response to advertising will…
Cheryl Druehl Retailers, Inc., must decide whether to build a small or a large facility at a new location in Fairfax. Demand at the location will either be low or high, with probabilities 0.3 and 0.7,respectively. If Cheryl builds a small facility and demand proves to be high, she then has the option of expanding the facility. If a small facility is built and demand proves to be high, and then the retailer expands the facility, the payoff is $230,000. If a small facility is built and demand proves to be high, but Cheryl then decides not to expand the facility, the payoff is $203,000. If a small facility is built and demand proves to be low, then there is no option to expand and the payoff is $250,000. If a large facility is built and demand proves to be low, Cheryl then has the option of stimulating demand through local advertising. If she does not exercise this option, then the payoff is $40,000. If she does exercise the advertising option, then the response to…
Cheryl Druehl Retailers, Inc., must decide whether to build a small or a large facility at a new location in Fairfax. Demand at the location will either be low or high, with probabilities 0.6 and 0.4, respectively. If Cheryl builds a small facility and demand proves to be high, she then has the option of expanding the facility. If a small facility is built and demand proves to be high, and then the retailer expands the facility, the payoff is $290,000. If a small facility is built and demand proves to be high, but Cheryl then decides not to expand the facility, the payoff is $253,000. If a small facility is built and demand proves to be low, then there is no option to expand and the payoff is $220,000. If a large facility is built and demand proves to be low, Cheryl then has the option of stimulating demand through local advertising. If she does not exercise this option, then the payoff is $35,000. If she does exercise the advertising option, then the response to advertising will…